• Communications for Statistical Applications and Methods
• /
• 제28권6호
• /
• pp.643-653
• /
• 2021

Few studies are found in literature on estimation of population quantiles using the method of ranked set sampling (RSS). The optimal RSS strategy is to select observations with at most two fixed rank order statistics from different ranked sets. In this paper, a near optimal unbalanced RSS model for estimating p^th(0 < p < 1) population quantile is proposed. Main advantage of this model is to use each rank order statistics and is distributionfree. The asymptotic relative efficiency (ARE) for balanced RSS, unbalanced optimal and proposed near-optimal methods are computed for different values of p. We also compared these AREs with respect to simple random sampling. The results show that proposed unbalanced RSS performs uniformly better than balanced RSS for all set sizes and is very close to the optimal RSS for large set sizes. For the practical utility, the near optimal unbalanced RSS is recommended for estimating the quantiles.

• Communications for Statistical Applications and Methods
• /
• 제18권1호
• /
• pp.147-153
• /
• 2011

In this paper a new sampling procedure for estimating the population mean is introduced. The performance of the new population mean estimator is discussed, along with its properties, and it is shown that the proposed method generates an unbiased estimator. The relative efficiency of the suggested estimator is computed, in regards to the simple random sample(SRS), and comparisons are made to the ranked set sampling(RSS) and extreme ranked set sampling(ERSS) estimators used for asymmetric distributions. The results indicate that the proposed estimator is more efficient than the estimators based on the ERSS. In addition, the folded ranked set sampling(FRSS) procedure has an advantage over the RSS and ERSS in that it reduces the number of unused sampling units.

• Communications for Statistical Applications and Methods
• /
• 제13권2호
• /
• pp.419-428
• /
• 2006

The method of Reverse Ranked Ordering-Set Sampling(RROSS) as an opposed Ranked Ordering-Set Sampling(ROSS) and Ranked-Set Sampling(RSS) is discussed. We propose the test statistic using sign test on RROSS. This method is effective when observations are expensive and measurement is perhaps destructive or invasive. This method obtains more informations than ROSS and RSS. The asymptotic relative efficiencies of RROSS with respect to ROSS and RSS are always greater than 1 for all sample sizes. We consider a simple model to describe the effect of imperfect judgment errors.

• Communications for Statistical Applications and Methods
• /
• 제14권3호
• /
• pp.641-648
• /
• 2007

We propose the new sampling method, called modified ranked ordering set sampling (MROSS). Kim and Kim (2003) suggested the sign test using the ranked ordering set sampling (ROSS), and showed that the asymptotic relative efficiency (ARE) of ROSS against RSS for sign test increases as sample size does. We propose the estimator for the population mean using MROSS. The relative precision (RP) of estimator of the population mean using MROSS method with respect to the usual estimator using modified RSS is higher, and when the underlying distribution is skewed, the bias of the proposed estimator is smaller than that of several ranked set sampling estimators.

• Communications for Statistical Applications and Methods
• /
• 제24권3호
• /
• pp.241-254
• /
• 2017

Drawing a sample can be costly or time consuming in some studies. However, it may be possible to rank the sampling units according to some baseline auxiliary covariates, which are easily obtainable, and/or cost efficient. Ranked set sampling (RSS) is a method to achieve this goal. In this paper, we propose a modified approach of the RSS method to allocate units into an experimental study that compares L groups. Computer simulation estimates the empirical nominal values and the empirical power values for the test procedure of comparing L different groups using modified RSS based on the regression approach in analysis of covariance (ANCOVA) models. A comparison to simple random sampling (SRS) is made to demonstrate efficiency. The results indicate that the required sample sizes for a given precision are smaller under RSS than under SRS. The modified RSS protocol was applied to an experimental study. The experimental study was designed to obtain a better understanding of the pathways by which positive experiences (i.e., goal completion) contribute to higher levels of happiness, well-being, and life satisfaction. The use of the RSS method resulted in a cost reduction associated with smaller sample size without losing the precision of the analysis.

• Communications for Statistical Applications and Methods
• /
• 제5권1호
• /
• pp.133-144
• /
• 1998

In this paper, we propose the two-sample test statistic using Wilcoxon signed rank test on ranked-set sampling(RSS) and obtain the asymptotic relative efficiencies(ARE) of the proposed test statistic with respect to Mann-Whitney-Wilcoxon statistic on simple random sampling(SRS), the Mann-Whitney-Wilcoxon statistic on RSS, sign statistic on RSS and Wilcoxon signed rank test on SRS. From the simulation works, we compare the powers of the proposed test statistic, Mann-Whitney-Wilcoxon statistic on RSS, the usual two-sample t statistic, sign statistic on RSS, where the underlying distributions are uniform, normal, double exponential, logistic and Cauchy distributions.

• Journal of applied mathematics & informatics
• /
• 제3권2호
• /
• pp.235-244
• /
• 1996

Ranked-set sampling is useful when measurements are destructive or costly to obtain but ranking of the observations is rel-atively easy. The Wilcoxon signed rank test statistic based on the ranked-set sample is considered. We compared the asymptotic relative efficiencies of the RSS Wilcoxon signed rank test statistics with respect to the SRS Wilcoxon signed rank test statistic and the RSS sign test statistic. Throughout the ARE's the proposed test statistic is superior to the SRS Wilcoxxon signed rank test statistic and the RSS sign test statistic.

• Journal of applied mathematics & informatics
• /
• 제41권2호
• /
• pp.449-468
• /
• 2023

This paper deals in the study of the estimation of the parameters of Erlang distribution based on rank set sampling and some of its modifications. Here we considered Maximum Likelihood (ML) and the Bayesian technique to estimate the shape and scale parameter of Erlang distribution based on RSS and its some modifications such as ERSS, MRSS, and MRSSu. The derivation for unknown parameters of Erlang distribution is well presented using normal approximation to the asymptotic distribution of ML estimators. But due to the complexity involves in the integral, the Bayes estimator of unknown parameters is obtained using MCMC method. Further, we compared the MSE of estimation in different sampling schemes with different set sizes and cycle size. A real-life data application is also given to illustrate the efficiency of the proposed scheme.